1. Field of the Invention
This invention relates to single crystals of the type ATiOXO.sub.4 wherein A is K, Rb, T1 or NH.sub.4 and X is P or As and to their use in electrooptic devices.
2. Background of the invention
Electrooptic devices utilizing the non-zero components of the second order polarizability tensor to achieve second harmonic generation, parametric amplification, the addition and subtraction of frequencies, tunable frequencies, modulation and the like of coherent electromagnetic radiation have been described by Albert A. Ballman, Gary D. Boyd and Robert C. Miller in U.S. Pat. No. 3,262,058, by J. A. Giordmaine and Robert C. Miller in U.S. Pat. No. 3,328,723, and by Satoshi Nanamatsu and Masakazu Kimura in U.S. Pat. No. 3,747,022.
Briefly, electromagnetic waves propagating in a crystal having nonlinear optical properties induce polarization waves with frequencies which are the sum and the difference of the frequencies of the exciting waves. These polarization waves can radiate electromagnetic waves having the frequencies of the polarization waves. The energy transferred to a radiated electromagnetic wave from a polarization wave depends on the magnitude of the component of the second order polarizability tensor involved since this tensor element determines the amplitude of the polarization wave and also on the distance over which the polarization wave and the radiated electromagnetic wave can remain sufficiently in phase, called the coherence length. The coherence length is given by .pi./(.DELTA. .kappa.) wherein .DELTA..kappa. is the difference between the wave vector of the radiated electromagnetic wave and the wave vector of the polarization wave. Phase matching occurs when the waves are completely in phase, that is when .DELTA..kappa. = 0. The condition .DELTA..kappa. = 0 can also be expressed as n.sub.3 .omega..sub.3 = n.sub.1 .omega..sub.1 .+-. n.sub.2 .omega..sub.2 wherein .omega..sub.3 = .omega..sub.1 .+-. .omega..sub.2 and where .omega..sub.1 and .omega..sub.2 are the frequencies of the incident light and .omega..sub.3 is that of the radiated optical wave and the n's are the corresponding refractive indices. The plus signs are appropriate when the sum frequency is the one of interest; the minus signs are appropriate when the difference frequency is the one of interest. A particular case which will be used as a simple example of nonlinear effects is second harmonic generation (SHG) where there is only one incident wave of frequency .omega. and .omega..sub.1 = w.sub. 2 = .omega. and .omega..sub.3 = 2.omega. .
The above phase matching conditions can be met, with birefringent crystals provided the refractive index difference between the ordinary and the extraordinary rays is sufficiently large to offset the change of refractive index with frequency, i.e., optical dispersion.
Generally phase matching is of two types:
Type I wherein the two incident waves have the same polarizations and
Type II wherein the two incident waves have orthogonal polarization.
Phase matching can be achieved by "tuning" the crystal in various ways.
1. By rotation of the crystal to vary the refractive indices.
2. By varying the temperature.
3. By application of an electric field.
4. By compositional variation.
A complication in this phase matching process is the fact that phase matching occurs only for certain crystallographic directions. If a light ray deviates from this phase-matched direction, a mismatch occurs and .DELTA..kappa. is no longer zero. For example, when collinear phase-matched SHG is used such a situation occurs if the alignment of the incoming beam and the phase-matched crystallographic direction is not exact or if the incoming beam is slightly divergent. In general .DELTA..kappa. will be a linear function of the deviation .DELTA..theta. from the phase-matched direction. This places a restriction on the allowable angular divergence since a useful coherence length must be maintained. In addition, because of the double refraction, the radiated electromagnetic wave and the polarization wave will in general propagate in different directions, termed "walk-off", thereby reducing the interaction distance. Phase matching under these unfavorable conditions is called "critical phase matching" (CPM). For certain crystallographic directions, .DELTA..kappa. does not vary linearly with the angular deviation .DELTA..theta., but rather varies as (.DELTA..theta.).sup.2. As a result, greater divergence from the phase-matched direction is allowable and no first-order " walk-off" occurs. Phase matching under these conditions is called "non-critical phase matching" (NCPM). The advantages of NCPM over CPM for practical devices are obvious. The indices of refraction can be adjusted by temperature variation or compositional variation in suitable cases so that phase matching occurs for crystallographic directions along which NCPM is possible. For biaxial crystals, NCPM conditions are possible for the SHG we have been discussing only when propagation is along certain of the principal axes of the optical indicatrix. (M. V. Hobden, J. Appl. Phys. 38, 4365 [1967])
The possibility of achieving one or more types of phase matching, and the appropriate orientation of the crystal to the incident wave depends on the existence of non-zero elements in the second order polarizability tensor. Depending on the point group symmetry of the crystal some elements will be identically zero, and equalities are imposed on other elements. The magnitude of the effects will depend on the magnitude of the non-zero elements.
Accordingly, there is a need in the art to provide crystals of different useful symmetry types capable of compositional variation, and preferably having non-linear electrooptic properties which are large in magnitude.
R. Masse and J. C. Grenier, Bull. Soc. Mineral Crystallogr. 94, 437-439 1971 have described the properties of MTiOPO.sub.4 wherein M is K, Rb or Tl in the form of fine crystalline powder.